You can buy concrete paint. This usually does a good job of covering up stains.
You can paint it with a solid paint or you can do a faux paint of brick or stone.

If I could add my two cents... Painting a concrete patio will always lead to paint chipping from wear and tear in a few years. Staining a patio will weather and over time the stain will fade. Long term I would suggest tile or flagstone over the patio will give you the longest consistent look.

There are some products that you can use to refinish concrete to look like stone I would try those. I know Home Depot carries Seal-crete check it out.